Despite three nights at Croke Park this weekend, the world's biggest boy band could be reaching the end of the line.

At first inspection, the idea that the world's biggest boyband are on borrowed time might sound preposterous. The shiniest quiffs in pop roll into Dublin today for a three-night Croke Park stand that will see them play to 150,000 fans. They are, by anyone's standards, at the summit of the music business: a five-headed profit machine that is defying the death rattle sweeping the industry elsewhere.

At first inspection, the idea that the world's biggest boyband are on borrowed time might sound preposterous. The shiniest quiffs in pop roll into Dublin today for a three-night Croke Park stand that will see them play to 150,000 fans. They are, by anyone's standards, at the summit of the music business: a five-headed profit machine that is defying the death rattle sweeping the industry elsewhere.

Look closer, though, and you will see, in their hour of triumph, the first cracks appearing. One Direction, band and brand, is four years old now: the hyperventilating tweenies who glommed onto them as 10-year-olds are about to turn 14, the age at which adolescents typically turn away from spoon-fed pop and start to explore music that reflects the person they are growing into. Also, after three number one albums and a 68-date stadium tour, where do you go? The answer, if pop history tells us anything, is down.

Since coming together on the 2010 season of X Factor, they have achieved all that is possible for a British-Irish pop affair: outselling The Beatles, breaking America, becoming so famous they are recognisable by silhouette and choice of hair-care product alone. The crucial distinction is that, unlike rock groups, boybands have a shelf life, few making it past five years.

Clever young men who have parlayed toothy grins and decent voices into globe-straddling ubiquity, the members of One Direction are no doubt perfectly aware of this. Which may be why they have started to think about life after the band. Especially cognisant of the big picture, it appears, is Harry Styles, the potential Robbie Williams/ Justin Timberlake in the line-up.

While loyal to One Direction, Styles knows where he wishes to be in the long term. At the beginning of 2014, the band quietly embarked on a three-month hiatus, during which they stayed assiduously clear of one another. In that time, Styles seemed determined to spread his wings creatively, working with Swords sop-rockers Kodaline and One Republic songwriter Ryan Tedder.

Indeed, sources quoted by the UK press have suggested Styles' very visible flirtations with other musicians have caused unease among his bandmates who, it is alleged, feel the dalliances have a destabilising effect.

"It's as if Harry isn't part of the group," one insider says. It's going to come to a head now because for the first time in months they are going to be spending every day together for this summer's tour." Concerns that Styles' may be considering his own direction were fuelled when a second source highlighted his recent decision to relocate to LA, an ocean and continent removed from Niall, Zayn et al.

The goal, the friend said, was to set himself up for a Justin Timberlake trajectory, parlaying boyband fame into enduring credibility.

"Harry prefers LA because he could be a real star over there. He has the big picture in mind and his bandmates know it. It's a matter of time before he goes solo."

Incredibly, One Direction are already one of the most long-in-the- tooth boybands of their era: The Wanted have just completed a farewell tour, JLS called it quits in 2013.

Even further back, it is generally forgotten that in their original incarnation Take That lasted a mere half decade.

The only boyband to ever face down the ticking clock of irrelevancy was Westlife.

As they survey the 80,000 audience at tonight's opening Croker date, One Direction may reflect that, once you reach the summit, you have to plummet earthward.

Of course, it is entirely possible their fanbase may give up on them before they give up on it. Anecdotally, there are suggestions that a chunk of the teenagers who bought – or badgered parents into buying – One Direction tickets last year may have already outgrown the heartthrobs.

"My daughter pestered me for tickets last year," one exasperated father said.

"She was 13 then. Now she's 14 and she wants to see the Arctic Monkeys."